多変量回帰・・・好きですか?
2025-05-27
古くから研究されつくされており、信頼感がある
多くの統計ソフトに入っており、行うのが簡単
解釈性が高く、分かりやすい
本当?
| n | missing | distinct | Info | Mean | pMedian | Gmd | .05 | .10 | .25 | .50 | .75 | .90 | .95 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 558 | 0 | 69 | 0.999 | 75.29 | 74.5 | 16.57 | 54.0 | 58.0 | 64.0 | 74.0 | 84.0 | 95.3 | 102.0 |
| n | missing | distinct | Info | Mean | pMedian | Gmd | .05 | .10 | .25 | .50 | .75 | .90 | .95 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 558 | 0 | 94 | 0.998 | 135.3 | 134.5 | 23.35 | 104.0 | 110.0 | 120.0 | 133.0 | 150.0 | 162.3 | 170.1 |
| n | missing | distinct | Info | Mean | pMedian | Gmd | .05 | .10 | .25 | .50 | .75 | .90 | .95 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 558 | 0 | 441 | 1 | 10181 | 10016 | 2813 | 6607 | 7200 | 8400 | 9792 | 11663 | 13610 | 14770 |
| n | missing | distinct | Info | Mean | pMedian | Gmd | .05 | .10 | .25 | .50 | .75 | .90 | .95 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 558 | 0 | 105 | 1 | 120.6 | 121 | 25.36 | 81.85 | 90.70 | 106.25 | 122.00 | 135.00 | 147.00 | 155.15 |
| n | missing | distinct | Info | Mean | pMedian | Gmd | .05 | .10 | .25 | .50 | .75 | .90 | .95 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 558 | 0 | 142 | 1 | 146.9 | 145 | 40.72 | 96 | 102 | 120 | 141 | 170 | 200 | 210 |
| n | missing | distinct | Info | Mean | pMedian | Gmd | .05 | .10 | .25 | .50 | .75 | .90 | .95 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 558 | 0 | 508 | 1 | 17634 | 17339 | 5765 | 10256 | 11341 | 14033 | 17060 | 20644 | 24536 | 26637 |
| n | missing | distinct | Info | Mean | pMedian | Gmd |
|---|---|---|---|---|---|---|
| 558 | 0 | 7 | 0.84 | 33.75 | 35 | 8.334 |
Value 10 15 20 25 30 35 40 Frequency 2 28 47 56 64 61 300 Proportion 0.004 0.050 0.084 0.100 0.115 0.109 0.538For the frequency table, variable is rounded to the nearest 0
| n | missing | distinct | Info | Mean | pMedian | Gmd | .05 | .10 | .25 | .50 | .75 | .90 | .95 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 558 | 0 | 103 | 1 | 119.4 | 119.5 | 24.64 | 82.0 | 91.0 | 104.2 | 120.0 | 133.0 | 146.0 | 154.1 |
| n | missing | distinct | Info | Mean | pMedian | Gmd | .05 | .10 | .25 | .50 | .75 | .90 | .95 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 558 | 0 | 78 | 0.999 | 78.57 | 78.5 | 16.86 | 53 | 60 | 69 | 78 | 88 | 97 | 104 |
| n | missing | distinct | Info | Mean | pMedian | Gmd | .05 | .10 | .25 | .50 | .75 | .90 | .95 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 558 | 0 | 132 | 0.999 | 156 | 154 | 35.03 | 110.0 | 120.0 | 133.2 | 150.0 | 175.8 | 200.0 | 211.1 |
| n | missing | distinct | Info | Mean | pMedian | Gmd | .05 | .10 | .25 | .50 | .75 | .90 | .95 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 558 | 0 | 484 | 1 | 18550 | 18267 | 5385 | 11346 | 12865 | 15260 | 18118 | 21239 | 24893 | 27477 |
| n | missing | distinct | Info | Mean | pMedian | Gmd |
|---|---|---|---|---|---|---|
| 558 | 0 | 8 | 0.941 | 30.24 | 30 | 10.55 |
Value 5 10 15 20 25 30 35 40 Frequency 7 7 55 73 71 78 62 205 Proportion 0.013 0.013 0.099 0.131 0.127 0.140 0.111 0.367For the frequency table, variable is rounded to the nearest 0
| n | missing | distinct | Info | Mean | pMedian | Gmd | .05 | .10 | .25 | .50 | .75 | .90 | .95 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 558 | 0 | 62 | 0.999 | 67.34 | 68 | 13.41 | 46.85 | 51.00 | 60.00 | 69.00 | 75.00 | 82.00 | 85.00 |
| n | missing | distinct |
|---|---|---|
| 558 | 0 | 2 |
Value female male Frequency 338 220 Proportion 0.606 0.394
| n | missing | distinct | Info | Mean | pMedian | Gmd | .05 | .10 | .25 | .50 | .75 | .90 | .95 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 558 | 0 | 54 | 0.994 | 55.6 | 57 | 10.71 | 32 | 40 | 52 | 57 | 62 | 65 | 66 |
| n | missing | distinct | Info | Mean | pMedian | Gmd | .05 | .10 | .25 | .50 | .75 | .90 | .95 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 558 | 0 | 60 | 0.992 | 65.24 | 67 | 12.38 | 40.0 | 49.7 | 62.0 | 67.0 | 73.0 | 76.0 | 80.0 |
| n | missing | distinct | Info | Sum | Mean |
|---|---|---|---|---|---|
| 558 | 0 | 2 | 0.64 | 172 | 0.3082 |
| n | missing | distinct | Info | Sum | Mean |
|---|---|---|---|---|---|
| 558 | 0 | 2 | 0.745 | 257 | 0.4606 |
| n | missing | distinct | Info | Sum | Mean |
|---|---|---|---|---|---|
| 558 | 0 | 2 | 0.553 | 136 | 0.2437 |
| n | missing | distinct | Info | Sum | Mean |
|---|---|---|---|---|---|
| 558 | 0 | 2 | 0.143 | 28 | 0.05018 |
| n | missing | distinct | Info | Sum | Mean |
|---|---|---|---|---|---|
| 558 | 0 | 2 | 0.138 | 27 | 0.04839 |
| n | missing | distinct | Info | Sum | Mean |
|---|---|---|---|---|---|
| 558 | 0 | 2 | 0.167 | 33 | 0.05914 |
| n | missing | distinct | Info | Sum | Mean |
|---|---|---|---|---|---|
| 558 | 0 | 2 | 0.123 | 24 | 0.04301 |
| n | missing | distinct | Info | Sum | Mean |
|---|---|---|---|---|---|
| 558 | 0 | 2 | 0.625 | 393 | 0.7043 |
| n | missing | distinct | Info | Sum | Mean |
|---|---|---|---|---|---|
| 558 | 0 | 2 | 0.699 | 206 | 0.3692 |
| n | missing | distinct |
|---|---|---|
| 558 | 0 | 3 |
Value heavy moderate non-smoker Frequency 122 138 298 Proportion 0.219 0.247 0.534
| n | missing | distinct | Info | Sum | Mean |
|---|---|---|---|---|---|
| 558 | 0 | 2 | 0.599 | 154 | 0.276 |
| n | missing | distinct | Info | Sum | Mean |
|---|---|---|---|---|---|
| 558 | 0 | 2 | 0.204 | 41 | 0.07348 |
| n | missing | distinct | Info | Sum | Mean |
|---|---|---|---|---|---|
| 558 | 0 | 2 | 0.399 | 88 | 0.1577 |
| n | missing | distinct | Info | Sum | Mean |
|---|---|---|---|---|---|
| 558 | 0 | 2 | 0.402 | 89 | 0.1595 |
| n | missing | distinct |
|---|---|---|
| 558 | 0 | 3 |
Value equivocal MI normal Frequency 176 71 311 Proportion 0.315 0.127 0.557
Logistic Regression Model
lrm(formula = death_01 ~ rcs(age, 4) * rcs(crea1, 4) + sex +
meanbp1 + hrt1 + resp1 + alb1, data = rhc_prep)
Frequencies of Missing Values Due to Each Variabledeath_01 age crea1 sex meanbp1 hrt1 resp1 alb1
0 0 0 0 0 0 0 2
| Model Likelihood Ratio Test |
Discrimination Indexes |
Rank Discrim. Indexes |
|
|---|---|---|---|
| Obs 5733 | LR χ2 425.17 | R2 0.098 | C 0.658 |
| 0 2013 | d.f. 20 | R220,5733 0.068 | Dxy 0.317 |
| 1 3720 | Pr(>χ2) <0.0001 | R220,3918.6 0.098 | γ 0.317 |
| max |∂log L/∂β| 8×10-5 | Brier 0.211 | τa 0.144 |
| β | S.E. | Wald Z | Pr(>|Z|) | |
|---|---|---|---|---|
| Intercept | -1.5123 | 1.1423 | -1.32 | 0.1855 |
| age | 0.0354 | 0.0285 | 1.24 | 0.2141 |
| age' | 0.0223 | 0.0640 | 0.35 | 0.7272 |
| age'' | -0.0605 | 0.4179 | -0.14 | 0.8848 |
| crea1 | 0.6915 | 1.2167 | 0.57 | 0.5698 |
| crea1' | -6.2577 | 22.2259 | -0.28 | 0.7783 |
| crea1'' | 10.0499 | 43.0148 | 0.23 | 0.8153 |
| sex=Male | 0.0882 | 0.0593 | 1.49 | 0.1366 |
| meanbp1 | -0.0043 | 0.0008 | -5.57 | <0.0001 |
| hrt1 | 0.0016 | 0.0008 | 2.06 | 0.0399 |
| resp1 | 0.0030 | 0.0021 | 1.42 | 0.1544 |
| alb1 | -0.1269 | 0.0426 | -2.98 | 0.0029 |
| age × crea1 | -0.0077 | 0.0306 | -0.25 | 0.8017 |
| age' × crea1 | -0.0256 | 0.0673 | -0.38 | 0.7034 |
| age'' × crea1 | 0.0802 | 0.4300 | 0.19 | 0.8521 |
| age × crea1' | 0.1578 | 0.5568 | 0.28 | 0.7769 |
| age' × crea1' | 0.3105 | 1.2149 | 0.26 | 0.7983 |
| age'' × crea1' | -0.5983 | 7.6709 | -0.08 | 0.9378 |
| age × crea1'' | -0.2886 | 1.0772 | -0.27 | 0.7888 |
| age' × crea1'' | -0.5863 | 2.3490 | -0.25 | 0.8029 |
| age'' × crea1'' | 1.0391 | 14.8179 | 0.07 | 0.9441 |
✕
◯
Call: glm(formula = death_01 ~ swang1, family = binomial(link = "logit"),
data = rhc_prep)
Coefficients:
(Intercept) swang1RHC
0.5309 0.2248
Degrees of Freedom: 5734 Total (i.e. Null); 5733 Residual
Null Deviance: 7433
Residual Deviance: 7418 AIC: 7422
通常のアウトカム式のみで一発勝負 ここはDoubly robustは使っちゃいけない
SUTVAの原理
例えば、Matching→G computation あるいは、元々のInclusionを入れて除外したあとにIPW→アウトカム式を入れる そうすることでDoubly robust estimationとなる
基本は、ドメイン知識を入れる ただし、どのような関係性かをみるのにはAICとか、尤度比検定をしても良いかも
すべてのモデルは誤っている。しかし、そのうちのいくつかは役に立つ。
| Parameter | Odds Ratio | 95% CI | p |
|---|---|---|---|
| (Intercept) | 0.25 | 0.11, 0.56 | < .001 |
| rx [Lev] | 0.92 | 0.66, 1.28 | 0.612 |
| rx [Lev+5FU] | 0.59 | 0.42, 0.83 | 0.003 |
| age | 1.01 | 1.00, 1.02 | 0.140 |
| sex | 1.03 | 0.78, 1.36 | 0.841 |
| obstruct | 1.41 | 1.00, 2.01 | 0.053 |
| perfor | 1.00 | 0.44, 2.29 | 0.997 |
| adhere | 1.65 | 1.11, 2.47 | 0.014 |
| surg | 1.47 | 1.07, 2.00 | 0.016 |
| nodes | 1.23 | 1.17, 1.30 | < .001 |
9716.5円/Cap x 4 x 365 = 1400万円/年
医療経済的にどう考えればいい?
estimand -> 誰に?
どれくらい?